I suggest following up on one of Shooter's questions, before rushing to shop for new or different parts. I think you might be OK with what you have, but let's verify.
You gave all specs for the original caps, but only some specs for the new caps that came in your kit. To clarify, you indicated 47uf, 47uf, 22uf, 47uf for the replacement caps. That is the capacitance of each capacitor in your kit - it means 47 micro farads, 22 micro farads, etc. Those specs seem fine.
But what about the
voltage of each? Please take a look at each of the caps in your replacement kit, and let us know the voltage on each. In particular, we're curious about the big 47uF caps.
The schematic of the power supply found at the link below, indicates that C52 - the first filter cap after the 6CA4 rectifier tube - normally sees 320 volts DC. It probably sees more than that at startup, and given today's higher household AC compared to the past, it might see more than that throughout regular use. So a 350 volt capacitor in that position might be OK, or it might be cutting it a little close.
https://1.bp.blogspot.com/-lGXMf-1Cew4/Xod0ekJn5DI/AAAAAAAADis/3nMcauGiPVwDt18GE2wM65Lsgw933ql5ACLcBGAsYHQ/s1600/ASR-120Power.gifIt would be nice - maybe not even a deal breaker, but nice to know - that the replacement cap for the first position, is at a higher spec than 350 volts. Please let us know what you see for voltage specs, on the replacement caps themselves.
About stuffing the can versus getting the amp working, I think Shooter means that you could probably get the amp in good working order first using what you have - including replacing these filter caps - before eventually deciding whether you want to stuff new caps into that old can, or shell out the additional possibly unnecessary money to buy an original-spec can.
As we have been discussing, there are several ways to do this right, from a functional standpoint. But there are choices you can make based on preference. Among your choices: (1) You can pull the can right out of the chassis, which takes some time and effort, and leaves a hole in the chassis which you probably have to plug up. Then you can install the new caps, using a few possible approaches. (2) You can leave the can in place, which gives you the same look from the outside view, up top. The amp looks the same from the exterior, in other words, because you're leaving the can and it's internal caps, in place. But then underneath, you install the new caps, using a few possible approaches. (3) You can do all the work to empty the can, stuff the new caps in, and wire them up.
I like choice 2, myself. It lets me preserve the amp's original look from the outside, and tends to be less work than the other two options.
You could try choice 2 to see if you get the amp working well. You already have the parts that should likely work. Then if you start feeling fussy later and really want to hollow out the can, or shop for a similar can with close to original specs, you could.
I use terminal strips, when implementing option 2. You mount them under the chassis, often somewhere near the bottom of the can caps you are updating. Then you can appropriately solder the new caps and existing wiring that went to the can cap, to the new terminal strips you have installed.
Hoffman (sponsor of this forum) sells terminal strips - scan this page:
https://hoffmanamps.com/MyStore/perlshop.cgi?ACTION=enter&template&thispage=BoardBuilding&ORDER_ID=!ORDERID!
Take a look at the 5-terminal options. Without thinking about it too much, or verifying for sure, I would think if you came up with two of those, you could install the caps in your kit just fine.